Solve for $x$ : $x^2 - 8x - 20 = 0$
Explanation: The coefficient on the $x$ term is $-8$ and the constant term is $-20$ , so we need to find two numbers that add up to $-8$ and multiply to $-20$ The two numbers $-10$ and $2$ satisfy both conditions: $ {-10} + {2} = {-8} $ $ {-10} \times {2} = {-20} $ $(x {-10}) (x + {2}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -10) (x + 2) = 0$ $x - 10 = 0$ or $x + 2 = 0$ Thus, $x = 10$ and $x = -2$ are the solutions.